You are both right and wrong.
You are right that God is not a man (male or female); man (male and female) was created in HIS image, not the other way around.
You are wrong that God has no male property by which He has basis to call Himself “He.” He refers to Himself in male terms throughout scripture, excepting as has been previously noted, some references to The Holy Spirit that I have not cataloged being not expressly male. God speaking prior to the First Advent of Christ speaks of Christ as “he.” Jesus speaking of God in the New Testament calls him “He.” The maleness of God is ubiquitous, though how it is expressed in the Person of the Divine remains mysterious to us, for we bear only his image, and that is sufficient; to bear His fullness is beyond our natural capacity.
The truth that St. Paul elucidated about there being “neither male nor female, Jew nor Greek (Gentile), slave nor free”; and Jesus’ own declaration that — in Heaven — mankind “neither marry nor are given in marriage,” but shall be as the angels — neither of these truths about physical gender obviate the eternal existence of “maleness” and “femaleness”; manifestations of which would continue, rightly, to be called “he” and “she.”
Excellent post and a fantastic capstone on this thread.
Well done!